31
The first stage DIT-FFT of a sequence x(n) is given by:
A)
\[X\left( k \right) = \left\{ \begin{array}{l}
G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\
G\left( {k + \frac{N}{2}} \right) - W_N^kH\left( {k + \frac{N}{2}} \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right)
\end{array} \right.\]
B)
\[X\left( k \right) = \left\{ \begin{array}{l}
G\left( k \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\
G\left( {k + \frac{N}{2}} \right) - W_N^kH\left( {k + \frac{N}{2}} \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right)
\end{array} \right.\]
C)
\[X\left( k \right) = \left\{ \begin{array}{l}
G\left( k \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\
G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right)
\end{array} \right.\]
D)
\[X\left( k \right) = \left\{ \begin{array}{l}
G\left( {k + N} \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\
G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right)
\end{array} \right.\]
Answer & Solution
Answer: Option
C
32
What is the value of magnitude frequency response of Butterworth low pass filter at Ω = 0 ?
A)
1
B)
$$\frac{1}{{\sqrt 2 }}$$
C)
0
D)
2
Answer & Solution
Answer: Option
A
33
The input-output relationship of a causal stable LTI system is given as y[n] = αy[n - 1] + βx[n]
A)
$$\alpha = 1 - \frac{\beta }{2}$$
B)
$$\alpha = 1 + \frac{\beta }{2}$$
C)
α = 2β
D)
α = -2β
Answer & Solution
Answer: Option
A
34
The linear time invariant system h(t) = (e-4t + e4t ).u(t) is . . . . . . . . and . . . . . . . .
A)
Causal, Unstable
B)
Noncausal, Unstable
C)
Causal, Stable
D)
Noncausal, Stable
Answer & Solution
Answer: Option
A
35
The unit sample response of a discrete system is 1, $$\frac{1}{2},\,\frac{1}{4},$$ 0, 0, 0 . . . For an input sequence 1, 0, 1, 0, 0, 0 . . ., what is the output sequence?
A)
$$1,\,\frac{1}{2},\,\frac{1}{4},\,\frac{1}{2},\,\frac{1}{4},\,0,\,0\,...$$
B)
$$1,0,\,\frac{1}{4},\,0,\,0\,...$$
C)
$$2,\,\frac{1}{2},\,\frac{5}{4},\,0,\,0\,...$$
D)
$$1,\,\frac{1}{2},\,\frac{5}{4},\,\frac{1}{2},\,\frac{1}{4},\,0,\,0\,...$$
Answer & Solution
Answer: Option
D
36
The output w[n] of the system shown in figure is \[\xrightarrow{{x\left[ n \right]}}\boxed{y\left[ n \right] = \sum\limits_{ - \infty }^n {x\left[ k \right]} }\xrightarrow{{y\left[ n \right]}}\boxed{w\left[ n \right] = y\left[ n \right] - y\left[ {n - 1} \right]}\xrightarrow{{w\left[ n \right]}}\]
A)
x[n]
B)
x[n - 1]
C)
x[n] - x[n - 1]
D)
\[\frac{1}{2}\] (x[n - 1]) + x[n]
Answer & Solution
Answer: Option
A
37
A matched filter having a frequency response $$H\left( f \right) = \frac{{1 - {e^{ - j2\pi fT}}}}{{j2\pi f}}$$ matches to:
A)
\[s\left( t \right) = \left\{ \begin{array}{l}
1,\,\,\,\,0 \le t \le T\\
0,\,\,\,\,{\rm{otherwise}}
\end{array} \right.\]
B)
\[s\left( t \right) = \left\{ \begin{array}{l}
- 1,\,\,\,\,0 \le t \le T\\
\,\,\,0,\,\,\,\,{\rm{otherwise}}
\end{array} \right.\]
C)
\[s\left( t \right) = \left\{ \begin{array}{l}
1 - \frac{t}{T},\,\,\,\,0 \le t \le T\\
\,\,\,\,\,0,\,\,\,\,{\rm{otherwise}}
\end{array} \right.\]
D)
\[s\left( t \right) = \left\{ \begin{array}{l}
- 1 + \frac{t}{T},\,\,\,\,0 \le t \le T\\
\,\,\,\,\,0,\,\,\,\,{\rm{otherwise}}
\end{array} \right.\]
Answer & Solution
Answer: Option
A
38
Auto-correlation function Rx (τ) of a stationary process X(t) is
A)
a deterministic function with maximum value at τ = 0
B)
a deterministic function which is periodic
C)
a stationary random process
D)
a periodic stationary process
Answer & Solution
Answer: Option
A
39
What is the ROC for the given signal?
A)
$$\left| z \right| > \frac{1}{2}$$
B)
$$\left| z \right| < \frac{1}{2}$$
C)
$$\left| z \right| < \frac{1}{3}$$
D)
$$\left| z \right| > \frac{1}{3}$$
Answer & Solution
Answer: Option
A
40
If the step response of a causal, linear time-invariant system is a(t), then the response of the system to a general input x(t) would be
A)
$$\int\limits_{{0^ + }}^t {\frac{{da\left( \tau \right)}}{{d\tau }}x\left( {t - \tau } \right)d\tau } $$
B)
$$a\left( 0 \right)x\left( t \right) + \int\limits_{{0^ + }}^t {\frac{{da\left( \tau \right)}}{{d\tau }}x\left( {t - \tau } \right)d\tau } $$
C)
$$x\left( 0 \right)a\left( t \right) + \int\limits_{{0^ + }}^t {x\left( \tau \right)a\left( {t - \tau } \right)d\tau } $$
D)
$$x\left( 0 \right)a\left( t \right) + \int\limits_{{0^ + }}^t {\frac{{da\left( \tau \right)}}{{d\tau }}x\left( {t - \tau } \right)d\tau } $$
Answer & Solution
Answer: Option
A
